THE ISOTHERMAL REGION, OR STRATOSPHERE 49
it loses as much energy by radiation as it gains by absorption. Furthermore, so long as its chemical nature remains the same, its coefficient of absorption is but little affected by even considerable changes in temperature. Therefore, whatever the nature of the object, since it is exposed to twice as much radiation when between the two planes as it is when facing but one, it must, in the former case, both absorb and emit twice as much energy as in the latter. Or, using symbols,
in which E% and EI are the quantities of heat radiated by the object per second, say, when between the two planes and -when facing but one, respectively. Again,
E, = X22Y2 and
Ei = .KiTY11
in which Tz and TI are the respective absolute temperatures of the object under the given conditions, and K and n its radiation constants.
For every substance there are definite values. of K and n which, so long as the chemical nature of the object remains the same, do not rapidly vary with change of temperature. Hence, assuming K% — K\ and n% = n\, we have, from the equation
From this it appears that there must be some minimum temperature T\ below which the radiation of the earth and lower atmosphere will not permit the upper atmosphere to fall, though what it is for a given value of T2 depends upon the value of n.
Presumably the radiation of the upper atmosphere is purely a thermal radiation, arid, therefore, in full agreement, as is the thermal radiation of water vapor, carbon dioxide, and certain other gases, with the Kirch-hoff1 law. In other words, the ratio of emission to the coefficient of absorption for any given wave length, presumably, is wholly a question of temperature, and is numerically equal to the radiation of a black body at the same temperature and wave length. In symbols,
T) -(*>
h A,« M
in which // is the incident energy, h the energy absorbed, and e the energy emitted by the body or gas in question at the wave length X and temperature t, and E the black-body emission at the same wave length and temperature, all per equal area and time.
1 PRINGSHEIM, "Congres International de Physique," 2; 127, Paris, 1900.